Here, \({U}\) , \(A\)  and \(f\) , stand for the average injection velocity, amplitude and frequency, respectively, of the external pulsatile perturbation. The radial distance, \(r\) , within the jet measured from its centreline \((y_0, z_0)\)  is \(r=\sqrt{\left(y-y_0\right)^2 + \left(z-z_0\right)^2}\) . The values for \(A\)  and \(f\)  are informed by the previous work of [1]} (e.g., \(A=0.05\)  m/s and \(f=20\)  Hz).
The numerical setup closely follows other computational studies; for example, we impose a free boundary condition on the walls of the computational domain to let the fluid freely enter or leave the boundaries [2]}, [1]}, [4]}. A pressure outflow boundary condition is applied on the right surface of the domain to allow the fluid to exit the domain. The solid nozzle is treated as a no-slip surface [5]}.
